Certificate for #15932 ⟨a, b | aba=bb, abbbb=b⟩

Completion settings:

• Reduction order:
  • Left-to-right recursive path with deg(a) = 0; deg(b) = 1

Axiom: aba=bb.

Flip LHS and RHS.

Referenced by [2], [3], [4], [5], [6], [12], [14].

Axiom: abbbb=b.

Reduce LHS:

Referenced by [4], [9].

Overlap of [1] bb=aba with [1] bb=aba:

Critical pair: baba=abab.

Flip LHS and RHS.

Referenced by [4], [5], [7].

Overlap of [3] abab=baba with [3] abab=baba:

Critical pair: abbaba=babaab.

Reduce LHS:

Flip LHS and RHS.

Referenced by [5], [8], [10].

Overlap of [4] babaab=b with [3] abab=baba:

Critical pair: babababa=bab.

Reduce LHS:

Flip LHS and RHS.

Referenced by [6], [7], [8], [10].

Overlap of [1] bb=aba with [5] bab=abaa:

Critical pair: babaa=abaab.

Reduce LHS:

Flip LHS and RHS.

Referenced by [7], [9], [10].

Overlap of [3] abab=baba with [5] bab=abaa:

Critical pair: abaabaa=babaab.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [8].

Overlap of [4] babaab=b with [5] bab=abaa:

Critical pair: abaaaab=b.

Reduce LHS:

Referenced by [11].

Simplify [2] aabaaba=b.

Reduce LHS:

Referenced by [10].

Overlap of [4] babaab=b with [9] aabaaaaa=b:

Critical pair: babb=baaaaa.

Reduce LHS:

Referenced by [11], [12].

Simplify [8] abaaaaaa=b.

Reduce LHS:

Defines rule #1.

Referenced by [12], [13].

Overlap of [1] bb=aba with [11] baaaaaaa=b:

Critical pair: bb=abaaaaaaaa.

Reduce LHS:

Reduce RHS:

Referenced by [13].

Overlap of [12] aba=baa with [11] baaaaaaa=b:

Critical pair: ab=baaaaaaaa.

Reduce RHS:

Defines rule #2.

Referenced by [14].

Simplify [1] bb=aba.

Reduce RHS:

Defines rule #3.